A recognized measure for judging the nature of correlated superconductors is through the change trend for \(T_c\)  and \(T_F\) . All the reported correlated superconductors discovered so far including cuprates, heavy fermion systems, organic materials [1]}, [2]}, and even twisted graphene [3]} follow a linear relationship between \(T_c\)  and \(T_F\) . The common characters for these superconductors are the existence of some competing order(s) and the strong electron correlation effect. Thus, the electron correlations are believed to be the major player for superconductivity in these systems. When adding the obtained \(T_c\)  and \(T_F\)  values for K\(_3\) C\(_{60}\)  in the map (Fig. 7), we find that this superconductor nicely follows the same linear trend as the other correlated superconductors but being very close to Ba\(_{1-x}\) K\(_x\) BiO\(_3\) . The trend itself classifies K\(_3\) C\(_{60}\)  as an unconventional correlated superconductor. The neighbourhood for Ba\(_{1-x}\) K\(_x\) BiO\(_3\)  and K\(_3\) C\(_{60}\)  implies that their superconductivity may be governed by the similar factors. For Ba\(_{1-x}\) K\(_x\) BiO\(_3\) , till recently it was found [4]} that the electron correlations enhance the electron-phonon coupling and they together contribute to the high \(T_c\)  in this system. It is reasonable to believe both the electron correlations and electron-phonon coupling jointly account for superconductivity in K\(_3\) C\(_{60}\) . This idea finds the support from the theoretical calculations on alkali-doped fullerides mainly focusing on Cs\(_{3}\) C\(_{60}\)  [5]}, where the electron-phonon coupling was found to enhance the electron correlations and they together gave the correct \(T_{c}\)  evolution trend with the unit cell volume, though the calculated \(T_{c}\)  is generally lower about 10 K than the experimental value. Since the strong coupling effect in K\(_3\) C\(_{60}\)  has been firmly established from high \(T_c\) , high \(H_{c2}\) (0), large \(2\Delta /k_BT_c\) , and the Raman data, the \(T_c\)  and \(T_F\)  relation derived from other parameters further suggests unconventional correlated superconductivity and the joint contributions from the electron-phonon coupling and electron correlations [6]}, [7]}. Recalling the unconventional isotope effect, the nice collaboration between the strong electron-phonon coupling and electron correlations is thus suggested to be responsible for the observed unconventional superconductivity in K\(_3\) C\(_{60}\) , both in a favorable way. This should be the base and constraints on the examinations of the existing theories and the future theory development for the mechanism of superconductivity for fullerides.
